Abstract
We combine SO(10) Grand Unified Theories (GUTs) with A4 modular symmetry and present a comprehensive analysis of the resulting quark and lepton mass matrices for all the simplest cases. We focus on the case where the three fermion families in the 16 dimensional spinor representation form a triplet of Γ3 ≃ A4, with a Higgs sector comprising a single Higgs multiplet H in the 10 fundamental representation and one Higgs field overline{Delta } in the overline{mathbf{126}} for the minimal models, plus one Higgs field Σ in the 120 for the non-minimal models, all with specified modular weights. The neutrino masses are generated by the type-I and/or type II seesaw mechanisms and results are presented for each model following an intensive numerical analysis where we have optimized the free parameters of the models in order to match the experimental data. For the phenomenologically successful models, we present the best fit results in numerical tabular form as well as showing the most interesting graphical correlations between parameters, including leptonic CP phases and neutrinoless double beta decay, which have yet to be measured, leading to definite predictions for each of the models.
Highlights
Modular forms are characterised by a positive integer level N and an integer weight k which can be arranged into modular multiplets of the homogeneous finite modular group ΓN ≡ Γ/Γ(N ) [3]
We focus on the case where the three fermion families in the 16 dimensional spinor representation form a triplet of Γ3 A4, with a Higgs sector comprising a single Higgs multiplet H in the 10 fundamental representation and one Higgs field ∆ in the 126 for the minimal models, plus one Higgs field Σ in the 120 for the non-minimal models, all with specified modular weights
The neutrino masses are generated by the type-I and/or type II seesaw mechanisms and results are presented for each model following an intensive numerical analysis where we have optimized the free parameters of the models in order to match the experimental data
Summary
In modular-invariant supersymmetric theories, the action is generally of the form. where K(τ, τ, ΦI , Φ I ) is the Kähler potential, and W(τ, ΦI ) is the superpotential. In modular-invariant supersymmetric theories, the action is generally of the form. Where K(τ, τ, ΦI , Φ I ) is the Kähler potential, and W(τ, ΦI ) is the superpotential. The action is required to be modular invariant. Under the action of Γ, the supermultiplets ΦI transform as [2]. Where −kI is the modular weight of ΦI , and ρI is a unitary representation of the finite modular group ΓN = Γ/Γ(N ). ΦIn. Modular invariance of W requires that YI1...In(τ ) should be a modular forms of weight kY and level N transforming in the representation ρY of ΓN , i.e., YI1...In (τ ) → YI1...In (γτ ) = (cτ + d)kY ρY (γ)YI1...In (τ ). The modular weights and the representations should satisfy the conditions kY = kI1 + .
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